In the case of the optical element holding device known from JP10206713 a plate-shaped first support can be pivoted with respect to a main support, which for example is oriented horizontally in the installed position, about the first axis, which then likewise extends horizontally. A second support is also pivotable with respect to the first support about a second axis, where the second axis is oriented parallel to the plate-shaped first support and thus likewise substantially horizontally. In the case of this optical element holding device a first and second actuating element for setting the respective pivoting positions are typically actuated perpendicularly to the plate-shaped first support, i.e. from above or from a vertical direction in the installed position.